Optical signals are distorted by the joint effects of dispersion and nonlinearity during their propagation in optical fiber. In most installed long-haul fiber communication systems, dispersion is typically compensated by periodically cascading two or more kinds of fiber with inverse dispersion parameters. With the advent of new inverse dispersion fibers (IDFs), wide-band dispersion flatness has been obtained by compensating for both dispersion and dispersion slope while minimizing the total polarization mode dispersion (PMD). In emerging coherent communication systems, dispersion can also be compensated using digital signal processing (DSP). As the technology of dispersion compensation matures, fiber nonlinearity effects, including self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM), become the limiting factor to further increase the spectral efficiency and transmission distance of long-haul fiber communication systems.
Methods such as optimized dispersion management, large effective area fiber, and new modulation formats have been investigated and employed in order to mitigate nonlinear effects. In addition to methods that mitigate nonlinearity, methods of compensating nonlinear impairments have been proposed. In dispersion-shifted fibers, nonlinear phase shift can be compensated with lumped nonlinear phase de-rotation based on the assumption that the intensity waveform remains unchanged throughout fiber propagation. However, lumped nonlinearity compensation performs poorly where there is significant interaction between nonlinearity and dispersion. In addition, nonlinearity pre-compensation at the transmitter side has been proposed for direct-detection systems.
Enabled by coherent detection, nonlinearity post-compensation via digital backward propagation (DBP) has attracted significant attention. Examples of DBP are described in U.S. Pub. No.: 20100239270, U.S. Pub. No.: 20100239262, U.S. Pub. No.: 20100239261, U.S. Pub. No.: 20100239254, and U.S. Pub. No.: 20090214215, each of which is incorporated by reference herein. DBP is typically implemented using the split-step method (SSM). Conventional digital backward propagation by means of the split-step method is based on the virtual division of the total transmission distance into short steps. In each step, the fiber dispersion is compensated with a linear operation, and the fiber nonlinearity is compensated with a nonlinear phase rotation which is usually proportional to the fiber nonlinear parameter γ, the optical intensity, and the effective fiber length of the step. In order for the split-step method to be accurate, a large number of steps are needed, especially for inter-channel nonlinearity compensation of WDM systems, resulting in a prohibitive computational load. In view of the computational intensity associated with split-step DBP, it would be desirable to have a more efficient method for compensating for fiber nonlinearity.